[jfengel]

We can't really talk about what's inside a black hole. From outside, it has a volume and a mass, and that's all there is to know.

We can say that any particle inside the horizon is inevitably headed to the center. (That's why we can't say any more: no other information can escape.) That does lead to a problem in that all of the mass would be concentrated at a single point at the center, whose density is division-by-zero.

But I wouldn't put too much weight on that. We already know from quantum mechanics that there isn't really any such thing as a "point". The math is still a problem, but the solution almost certainly lies in that direction.